What basic testing should my Dr be doing?

I am planning to request the tests below next visit and want recommendations for any others I should be asking for. Currently he is watching only the free test levels. Yes, I know the Dr should be doing this, and long term I want to find a good endocrinologist, but for now, with insurance and geographical limitations, I have what I have. On the plus side he is very receptive to my requests and willing to talk about options. Any recommendations are appreciated. Thanks.